Download Overjet at the Anterior and Posterior Segments: Three

Original Article
Overjet at the Anterior and Posterior Segments:
Three-Dimensional Analysis of Arch Coordination
Yoon-Ah Kooka; Mohamed Bayomeb; Soo-Byung Parkc; Bong-Kuen Chad;
Young-Wuk Leee; Seung-Hak Baekf
ABSTRACT
Objectives: To compare the amounts of anatomical overjet measured from facial axis (FA) points
with the amounts of bracket overjet measured from bracket slot center (BSC) points.
Materials and Methods: The samples consisted of 27 subjects with normal occlusion whose
models were fabricated with a three-dimensional (3D) scanner and the 3Txer program (Orapix Co
Ltd, Seoul, Korea). 3D virtual brackets (0.022⬙ Slot, MBT setup, 3M Unitek, Monrovia, Calif) constructed with a 3D-CAD program were placed on an FA point with the 3Txer program. The arch
dimension and the amounts of overjet from FA and BSC points were measured. Paired t-tests
and analysis of variance (ANOVA) tests were used for statistical analysis.
Results: No significant difference in arch width and depth was observed between FA and BSC
points. Although the amounts of overjet measured from FA points showed homogenous distribution, a tendency to decrease from the anterior segment (2.3 mm) to the posterior one (2.0 mm)
was noted. However, the amounts of overjet measured from BSC points were variable, especially
in the premolar and molar areas. Significant discrepancies in the amounts of overjet in most of
the areas between FA and BSC points (more than P ⬍ .05), except the lower second premolar
and second molar areas, were reported, even though insets and offsets are part of the prescription
for the base of straight-wire appliance (SWA) brackets.
Conclusions: The hypotheses that the amount of overjet measured from BSC points was 3 mm
through the whole segments and that distribution of the amounts of overjet from BSC points was
the same as that from FA points were rejected. (Angle Orthod. 2009;79:495–501.)
KEY WORDS: Overjet; Arch coordination; Facial axis point; Bracket slot center point
INTRODUCTION
face anatomy and maxillary/mandibular relationships,
tissue rebound, and biomechanical inefficiency of the
orthodontic appliances.1
The individualized prescription of the preadjusted
appliance, which could change the orientation of the
bracket slot relative to the labial or buccal surface of
each tooth, and the customized and coordinated arch
form might facilitate attainment of treatment goals and
increase the chance that stability will be improved.1,2
Coordination between the upper and lower arches
is one of the most important aspects of achieving stable functional and esthetic results during orthodontic
treatment. Because a transverse discrepancy could induce an adverse periodontal response, unstable dental camouflage, and functional and esthetic problems,3–6 maintenance of an adequate overjet during
treatment is essential.
Different and diverse landmarks such as the incisal
edge and cusp tip,7–11 centers of gravity (centroids) of
the occlusal surfaces,12 contact points, and clinical
bracket points based on mandibular tooth thickness
data13,14 have been used for measurement of arch form
Results of orthodontic treatment might fall short of
clinicians’ expectations for several reasons, including
inaccurate bracket placement, variations in tooth surAssociate Professor, Department of Orthodontics, Kangnam
St. Mary’s Hospital, The Catholic University of Korea, Seoul, Korea.
b
Graduate student, Department of Orthodontics, The Catholic
University of Korea, Seoul, Korea.
c
Professor, Department of Orthodontics, College of Dentistry,
Pusan National University, Pusan, Korea.
d
Professor, Department of Orthodontics, College of Dentistry,
Kangnung National University, Kangnung, Korea.
e
Private practice, Gyeongbuk, Korea.
f
Associate Professor, Department of Orthodontics, School of
Dentistry, Seoul National University, Seoul, Korea.
Corresponding author: Dr Seung-Hak Baek, Department of
Orthodontics, School of Dentistry, Dental Research Institute,
Seoul National University, Yeonkun-dong #28, Jongro-ku, Seoul,
South Korea 110-768, South Korea
(e-mail: [email protected])
a
Accepted: June 2008. Submitted: April 2008.
2009 by The EH Angle Education and Research Foundation,
Inc.
DOI: 10.2319/041108-205.1
495
Angle Orthodontist, Vol 79, No 3, 2009
496
and dimension. However, these landmarks did not represent the real alignment of the brackets and eventually of the archwires.
With rapid advances in three-dimensional (3D) virtual technology, most parameters of the 3D virtual
models could be measured as reliably and accurately
as those of the plaster models.15,16 Moreover, 3D software programs currently on the market, such as Invisalign (Align Technology Inc, Santa Clara, Calif),17
SureSmile (OraMetrix Inc, Dallas, Tex),18 and 3Txer
(Orapix Co Ltd, Seoul, Korea), can define the facial
axis (FA) point19 and perform virtual setup and bracket
placement on 3D virtual models. However, for precise
arch coordination, alignment of the bracket slots on the
teeth rather than alignment of FA points is needed.
Also, accurate positioning of the bracket slot center
(BSC) point may be possible in the 3D virtual study
rather than in the plaster models.
McLaughlin et al20 proposed that the upper archwire
should be coordinated with the lower one and should
be 3 mm wider than the lower one based on imprints
of brackets in the wax bite. Although Braun et al21 used
the spatial coordinates of the labial and buccal dental/
bracket interfacing surfaces in the upper and lower
arches, information about arch coordination with ‘‘3
mm’’ overjet through whole areas between the upper
and lower bracket slots is lacking.
The purposes of this study were to compare the
amounts of overjet measured from the FA points with
amounts measured from the BSC points in 3D virtual
models, and to provide a guideline for proper arch coordination. Therefore, two null hypotheses were postulated: the amount of overjet measured from BSC
points was 3 mm through the whole segments, and
distribution of the amounts of overjet from BSC points
was the same as from FA points.
KOOK, BAYOME, PARK, CHA, LEE, BAEK
Figure 1. (A) The right side view of the facial axis (FA) points
marked on three-dimensional (3D) virtual models. (B) The right side
views of the bracket slot center (BSC) points in 3D virtual brackets
and tubes (0.022⬙ Slot, MBT setup, 3M Unitek Co, Monrovia, Calif)
placed on the FA points of 3D virtual models. The FA point is the
facial axis point, which is defined as the point on the facial axis that
separates the gingival half of the clinical crown from the occlusal
half. The BSC point is defined as the junction of the midtransverse,
midsagittal, and midfrontal planes of the bracket slot.
MATERIALS AND METHODS
The samples consisted of Korean young adults with
normal occlusion (N ⫽ 27; 15 male and 12 female;
mean age, 23 years 5 months; age range, 20 to 25
years), to avoid the influence of growth- and malocclusion type–related bias. Inclusion criteria were as follows:
•
•
•
•
Angle’s Class I canine and molar relationships
ANB ⬎0⬚ and ⬍4⬚
Normal overbite and overjet (⬎0 mm, ⬍4 mm)
Minor arch length discrepancy (⬍3 mm of crowding,
⬍1 mm of spacing)
• Flat or slight curve of Spee (⬍2 mm)
• Absence of deviations in the dental midline and buccal crossbite
• Permanent dentition with normal tooth size and
shape, except third molars
Angle Orthodontist, Vol 79, No 3, 2009
• No history of previous orthodontic treatment
• No restorations extending to the contact areas, cusp
tips, or incisal edges
The 3D virtual maxillary and mandibular models
were fabricated with a 3D scanner (Orapix; 20 ␮m
units resolution) and the 3Txer program, version 1.9.6
(Orapix). FA points19 were marked on the whole dentition in both arches with the 3Txer program (Orapix)
(Figure 1A,B).
The 3D virtual straight wire appliance brackets
(0.022⬙ Slot, MBT setup, 3M Unitek, Monrovia, Calif),
which were fabricated by a 3D-CAD program (Solid
Edge, version 15, Siemens PLM Software, Plano, Tex)
according to the manufacturer’s prescription and measurement by digital Vernier calipers (500-18-20, Mitutoyo, Tokyo, Japan; accuracy, 0.01 mm), were placed
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3D ANALYSIS OF OVERJET AND ARCH COORDINATION
Table 1. Definition of Arch Dimension Variablesa
Arch Dimension Variables
Intercanine width, mm
Inter-first premolar width, mm
Inter-first molar width, mm
Canine depth, mm
Definition
FA
BSC
FA
BSC
FA
BSC
FA
BSC
Molar depth, mm
FA
BSC
Canine width/depth ratio
Molar width/depth ratio
a
FA
BSC
FA
BSC
Distance between the FA points of the right and left lower canines
Distance between the BSC points of the right and left lower canines
Distance between the FA points of the right and left lower first premolars
Distance between the BSC points of the right and left lower first premolars
Distance between the FA points of the right and left lower first molars
Distance between the BSC points of the right and left lower first molars
Shortest distance from a line connecting the FA points of the right and left lower canines to the
midpoint between the FA points of the right and left lower central incisors
Shortest distance from a line connecting the BSC points of the right and left lower canines to the
midpoint between the BSC points of the right and left lower central incisors
Shortest distance from a line connecting the FA points of the right and left lower first molars to the
midpoint between the FA points of the right and left lower central incisors
Shortest distance from a line connecting the BSC points of the right and left lower first molars to
the midpoint between the BSC points of the right and left lower central incisors
Ratio between lower canine width and depth from measurement using FA points
Ratio between lower canine width and depth from measurement using BSC points
Ratio between lower first molar width and depth from measurement using FA points
Ratio between lower first molar width and depth from measurement using BSC points
FA indicates facial axis; BSC, bracket slot center.
on the FA point with use of the BSC point and the
3Txer program (Orapix) by one investigator (B.M.),
who had adequate experience in 3D technology (Figure 1C,D). To guarantee precise placement of the 3D
virtual brackets on the tooth surface, bracket movement was begun at the level of 0.1 mm and under
check of the collision test to prevent unnecessary premature contact between the bracket and the tooth surface. In addition, each 3D virtual cast was checked
from the inside to verify the position of the bracket in
relation to the tooth surface.
The transverse direction was set as the x-axis, the
anteroposterior direction the y-axis, and the vertical
line perpendicular to the x and y planes, the z-axis.
The xy plane was formed from the FA point or the BSC
point of the lower right central incisor and the FA
points or the BSC points of the lower right and left first
molars.
Arch dimensions, including arch width and depth,
were measured with use of the FA and BSC points as
follows:
• The FA point on the upper right second molar was
set as the origin of the x and y axes.
• Five linear and two ratio variables for the arch dimension were measured and calculated (Table 1
and Figure 2).
Amounts of overjet at the anterior and posterior segments were measured with use of the FA and BSC
points as follows:
• The x and y coordinates for FA points or BSC points
of each case were inputted into a mathematical software program (MATLAB 7.5 [R2007b], The
MathWorks Inc, Natick, Mass) to draw the best fitting
curve that represents the arch, in accordance with
the fourth-degree polynomial equation (f(x) ⫽ ax 4 ⫹
bx3 ⫹ cx2 ⫹ dx ⫹ e) (Figure 3).2,11,12,22
• Overjet variables, which were defined as the tangent
and the shortest distance from the FA points or from
the BSC points of the lower teeth to the upper arch,
were measured with the 3Txer program, version
1.9.6 (Orapix) (Figure 3).
Measurements were taken by a single operator to
eliminate interoperator variability. All variables of the
five cases were reassessed after 2 weeks by the same
operator, so intraoperator variability could be evaluated. Because the Wilcoxon signed rank test revealed
no statistically significant difference between the two
assessments (P ⬎ .05), the first set of measurements
was used.
Because no statistically significant difference was
seen in the arch dimensions and the overjet between
right and left sides and between male and female subjects, the data were combined.
Paired t-tests were done to compare arch dimension
variables and amounts of overjet at the anterior and
posterior segments between the FA points and the
BSC points. A one-way analysis of variance (ANOVA)
test was performed to assess the differences in
amounts of overjet among these areas according to
FA and BSC points, respectively; data were verified
with Tukey’s post hoc test.
RESULTS
For arch dimension variables, no significant difference was observed between the FA points and the
BSC points in both upper and lower arches (Table 2).
Angle Orthodontist, Vol 79, No 3, 2009
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KOOK, BAYOME, PARK, CHA, LEE, BAEK
Figure 2. (A and B) Arch dimension variables measured from the facial axis (FA) points (the upper row). (C and D) Arch dimension variables
measured from the bracket slot center (BSC) points (the lower row). 1 indicates canine depth; 2, intercanine width; 3, molar depth; 4, interfirst molar width; and 5, inter-first premolar width.
In overjet measurement based on FA points, the
amounts of overjet showed homogenous distribution
according to ANOVA and Duncan tests (Table 3).
However, a tendency to decrease from the anterior
segment (⬃2.3 mm) to the posterior one (⬃2.0 mm)
was noted (Table 3 and Figure 4). Amounts of overjet
measured from the BSC points showed a tendency
toward greater variation through the whole dentition
than was seen with the FA points, and differences between the lower first premolar and second premolar
areas and between the lower second premolar and
first molar areas were reported (1.6 mm vs 2.1 mm;
2.1 mm vs 1.5 mm, respectively; Table 3 and Figure
4). Therefore, the hypothesis that the amount of overjet measured from BSC points was 3 mm through the
whole segments was rejected.
Significant discrepancies in amounts of overjet in
most areas between FA and BSC points were noted
(P ⬍ .05 in the lower central incisor area, lower lateral
Angle Orthodontist, Vol 79, No 3, 2009
incisor area, lower canine area, and lower first premolar area; P ⬍ .01 in the lower first molar area; Table
3 and Figure 4), even though insets and offsets are
part of the prescription for the base of straight-wire
appliance (SWA) brackets. Therefore, the hypothesis
that the distribution of amounts of overjet from BSC
points was the same as from FA points was rejected.
DISCUSSION
In addition to arch coordination, amounts of overjet
in the anterior and posterior segments of the dental
arches could be related to torque, labiolingual or buccolingual offset, marginal ridge relationships, and occlusal function such as incisal guidance and working
and nonworking side interference.
Cordato23,24 reported on a mathematical model that
could calculate the overjet of the anterior segment according to the sum of tooth widths in each arch, spac-
499
3D ANALYSIS OF OVERJET AND ARCH COORDINATION
Figure 3. Overjet variables were defined as the tangent and the
shortest distance from the facial axis (FA) points or from the bracket
slot center (BSC) points of the lower teeth to the upper arch. The
best fitting curves of the upper and lower arches were established
by the fourth-degree polynomial quation f(x) ⫽ ax 4 ⫹ bx 3 ⫹ cx 2 ⫹
dx ⫹ e. OJCI means overjet at the lower central incisor area; OJLI,
overjet at the lower lateral incisor area; OJC, overjet at the lower
canine area; OJP1, overjet at the lower first premolar area; OJP2,
overjet at the lower second premolar area; OJM1, overjet at the
lower first molar area; and OJM2, overjet at the lower second molar
area.
ing, crowding, angle of the arc of each arch, and the
anteroposterior buccal relation. Cordato25 insisted that
changes in overjet and overbite during and after orthodontic treatment could be predicted on the basis of
tooth thickness and angles of the upper teeth. Mutinelli
et al26 showed that different amounts of arch length
could be gained through proclination of the anterior
teeth (controlled tipping vs uncontrolled tipping) and
eventual change of the overjet without modification to
the arch width. However, few studies were undertaken
to analyze the overjet of the dental arches, especially
in the posterior segment.
Investigating the alignment of bracket slots on the
teeth seems to be a prerequisite to checking coordination of the upper and lower arches. However, previous studies that have used the incisal edge and the
cusp tip,7–11,26 centers of gravity (centroids) of the occlusal surfaces,12 and contact points and clinical bracket points based on mandibular tooth thickness data13,14
might not be related to alignment of the bracket in association with the ‘‘line of occlusion.’’ If the landmark
on the crown is located at a place far from the FA
point, this can influence amounts of overjet in keeping
with changes in crown inclination and angulation. Be-
Table 2. Comparison of the Arch Dimension Variables Between the Facial Axis Point and the Bracket Slot Center Point
Maxilla
Facial Axis
Intercanine width, mm
Inter-first premolar width, mm
Inter-first molar width, mm
Canine depth, mm
Molar depth, mm
Canine width/depth ratio
Molar width/depth ratio
Mandible
Bracket Slot Center
Facial Axis
Bracket Slot Center
Mean
SD
Mean
SD
Sig.*
Mean
SD
Mean
SD
Sig.*
38.13
47.14
58.94
8.39
30.17
4.58
1.96
1.54
2.01
2.49
0.77
1.52
0.42
0.13
38.51
47.54
59.95
8.43
30.94
4.59
1.94
2.05
2.22
2.75
0.66
1.88
0.4
0.15
NS
NS
NS
NS
NS
NS
NS
29.1
39.43
53.57
4.66
25.89
6.51
2.08
1.53
2.36
2.26
0.96
1.82
1.36
0.17
29.61
39.83
54.95
4.88
26.05
6.31
2.12
1.78
2.28
2.81
0.98
1.75
1.36
0.17
NS
NS
NS
NS
NS
NS
NS
* Paired t-tests were performed. Sig. indicates significance; NS, not significant; and SD, standard deviation.
Table 3. Comparison of the Overjet Between the Facial Axis Point and the Bracket Slot Center Point*
Facial Axis Pointa
Bracket Slot Center Pointb
Overjet (coordination distance)
Mean
SD
Mean
SD
P Value
Lower central incisor area (CI)
Lower lateral incisor area (LI)
Lower canine area (C)
Lower first premolar area (P1)
Lower second premolar area (P2)
Lower first molar area (M1)
Lower second molar area (M2)
Duncan multiple comparison test
2.34
2.31
2.19
2.05
2.00
1.97
1.98
0.89
0.72
0.72
0.64
0.48
0.45
0.74
1.73
1.77
1.80
1.61
2.05
1.50
1.86
0.80
0.91
0.86
0.72
0.58
0.51
0.75
.0112*
.0155*
.0382*
.0123*
.7577
.0043**
.5160
NS
NS
* Paired t-test was performed. P ⬍ .05; ** P ⬍ .01; SD indicates standard deviation; NS, not significant.
a
ANOVA test did not show a significant difference in the amounts of overjet measured from the facial axis point among whole areas (P ⫽
.2062).
b
ANOVA test did show significant difference in the amounts of overjet measured from the bracket slot center point among whole areas (P
⫽ .1869). However, Duncan test showed marginal difference (P ⫽ .0590) in (M1, P1, CI, LI, C, M2) ⬍ (P1, CI, LI, C, M2, P2).
Angle Orthodontist, Vol 79, No 3, 2009
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KOOK, BAYOME, PARK, CHA, LEE, BAEK
Figure 4. Comparison of the overjet at whole areas between the FA points and the BSC points.
cause the 3D virtual brackets used in the present
study were placed on the FA points, the BSC points
seemed to be less affected by changes in crown inclination and angulation than other landmarks used in
previous studies.7–14,26
The finding of a tendency toward a decreased
amount of overjet from the anterior segment (⬃2.3
mm) to the posterior one (⬃2.0 mm) in the FA points
(Table 3 and Figure 4) means that the arc of the posterior segment becomes relatively narrower than the
anterior one in the upper arch. This finding is consistent with those of Ferrario et al,11 who stated that the
upper arch showed a ‘‘mixed’’ elliptical (anterior teeth)
plus parabolic (postcanine teeth) interpolation of buccal cusp tips (central incisor to second molar).
Because the difference in the amount of overjet between anterior and posterior segments from FA points
was 0.3 mm (the value was obtained by subtraction
between 2.3 mm of the anterior segment and 2.0 mm
of the posterior one; Table 3) and values for the overjet
in the anterior segment from BSC points were approximately 1.8 mm (Table 3), the amounts of overjet in
the posterior segment from BSC points seemed to be
approximately 1.5 mm to achieve arch coordination
between upper and lower archwires. Therefore, it
might be recommended that the slight amount (around
a half millimeter) of the offset bend be added to the
second premolar area and second molar area in the
archwire to allow proper arch coordination.
The finding that there was a significant difference in
the amounts of overjet between FA points and BSC
points (P ⬍ .05 in the lower central incisor area, lower
lateral incisor area, lower canine area and lower first
premolar area; P ⬍ .01 in the lower first molar area;
Angle Orthodontist, Vol 79, No 3, 2009
Table 3 and Figure 4) and the finding that there were
significant differences in the amount of overjet between the lower first premolar and second premolar
areas and between the lower second premolar and
first molar areas from BSC points (⬃0.4 to ⬃0.5 mm;
Table 3 and Figure 4) could affect the amount of overjet in the finishing stage. These differences could be
compensated for by wire bending in the finishing
stage, by production of new brackets that have an individualized bracket base thickness, or by individualization of resin thickness under the bracket base for
indirect bonding.
Too much wire bending and adjustment of stainless
steel archwires in the finishing stage to restore a more
natural arch form and size and to obtain solid interdigitation of occlusion might result in deleterious tissue
effects.21 Therefore, evaluation of the relationship between the position of 3D virtual brackets and 3D virtual
setup models could help clinicians understand the
possible ‘‘round tripping’’ movement of teeth in the finishing stage.
Because the present study used a 3D virtual MBT
bracket (0.022⬙ Slot, 3M Unitek), other brackets should
be included to provide a guideline regarding amounts
of overjet used in future studies. In addition, because
racial differences in anatomical variation and dimensions of tooth material and arch may be seen,9 additional study of ethnic samples from multicenters is recommended.
CONCLUSIONS
• Although the amounts of overjet in the best fitting
curve established from the FA points showed ho-
3D ANALYSIS OF OVERJET AND ARCH COORDINATION
mogenous distribution, a tendency to decrease from
the anterior segment (2.3 mm) to the posterior one
(2.0 mm) was noted.
• Statistically significant differences were seen in the
amounts of overjet in most areas in the best fitting
curve between the FA and BSC points (more than P
⬍ .05), except in the lower second premolar and
second molar areas.
• To get proper arch coordination between upper and
lower archwires, wire bending in the finishing stage,
production of new brackets that have an individualized bracket base thickness, or individualization of
resin thickness under the bracket base for indirect
bonding might be recommended.
ACKNOWLEDGMENTS
This study was supported in part by the Alumni Fund of the
Department of Dentistry and Graduate School of Clinical Dental
Science, Catholic University of Korea. The authors would like to
thank Dr Kwang-Yoo Kim, Mr Dong-Soo Cho, Mr Seok-Jin Kang,
and the Orapix team for providing valuable technical advice.
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